1)I have a collection of "Enemy" objects that I check each iteration of the game loop to make sure the bullet hasn't collided with any of them. However, I just can't shake the feeling that there must be a better way than looping through them all and going "Has the bullet hit this one?".
With space invaders, the space aliens nicely form a regular row, making it easy to shoot them down 
The trick is to first do a rough estimate. In this case put a grid of rectangles onto the aliens, and decide which grid cell is the interesting one. No need to check all the other rectangles.
The grid starts at from the top-left alien position. From that point you can compute the position of all other aliens. The other way around, by subtracting pullet position from the position of the top-left alien, you can compute which alien it should hit, if any, ie
alien_width = 50; // Every 50 pixels, you have a new alien next to the previous one (just random example numbers)
alien_height = 40; // One row of aliens is 40 pixels high (another example number)
alien_topleft = (100, 110);
bullet = (220, 140);
column = (220 - 100) / 50 = 4; // Integer division, truncate fraction away.
row = (140 - 110) / 40 = 0;
Thus the alien 0 rows down from the top alien row, and 4 columns to the right in that row is where the bullet is. Now just check that one alien for precise hit, and you're done.
2)Once the bullet has struck said "Enemy" object it removes it from the collection and the game carries on. How should I handle the "Explosion"? Without having to slow/stop the game while the "Boom" runs.
You are moving and drawing the bullet every frame, right?
An explosion is the same, except you draw a different picture each frame, first frame shows small but deep ornage fire ball, second and third one show expanding fire ball, and then you get a series of frames where the fireball becomes deep red,and reduces size. So you have say 6 or 7 different images, showing a fire ball at different point in time during the explosion. Now if you draw these after each other at the same spot (each frame the next image), it looks like a 'real' explosion.
You could do the same with aliens or with bullets, instead of rendering the same image each time, pick a different one each frame. Then you have animated aliens and bullets.
if you where using the proper "Space Invaders" implementation but they way I work I am never going to learn typing in someone else's code
If you really type it, and try to understand it while you type, you do learn from it. It may now be a good time to study how your solution is different from their solution (I don't think there is a single proper solution; all solutions that implement the game are equivalent.)
